Suppose that the forward premium equals the conditional expectation of the future rate of appreciation of the foreign currency relative to the domestic currency
If we form the average realized rate of appreciation from a large sample of data and compare it to the average forward premium, what should be true?
If we impose the assumption of rational expectations, we know that we can decompose the realized rate of appreciation into the conditional expectation of the future rate of appreciation plus an error term that has a mean of zero. Therefore, the average of the realized rate of appreciation from a large sample of data should equal the average of the conditional expectations of the rate of appreciation. If the forward premium on the foreign currency at each moment in time equals the conditional expectation of the future rate of appreciation of the foreign currency relative to the domestic currency at that moment in time, the average or mean of the forward premium should be equal to the average of the realized rate of appreciation from a large sample of data.
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